A reduced hamiltonian model for U(∞) gauge theories

A reduced version of the Kogut-Susskind gauge theory is presented for U(∞) gauge theories. The reduced hamiltonian , where V_ij=trU_iD_iD_jD_j(U_iD_j) ⁺ (U_iD_j)⁺, is obtained by representing the group of space translations in the diagonal part of U(∞) U(∞). The space of states is invariant to the reduced gauge transformation U_i→ωU_iD_iω⁺D_i⁺ and the scalar product carries a gauge invariant constraint on U_i The hamiltonian is also expr essed in terms of the string variables of Bars. We present the linear potential between static quarks at strong coupling and sketch the weak coupling expansion.